Numerical integration: Difference between revisions
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(→{{header|J}}: Extend examples) |
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size * +/ 2 u\ a + size * i.>:steps |
size * +/ 2 u\ a + size * i.>:steps |
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rectangle=: adverb define |
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u -: +/ y |
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simpson=: adverb define |
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(6 %~ [: +/ 4&*@u@-:@(+/) , u) y |
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)</lang> |
)</lang> |
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| ⚫ | |||
Integrate <code>square</code> (<code>*:</code>) from 0 to pi in 10 steps using various methods. |
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<lang j> |
<lang j> |
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*: rectangle integrate 0 1p1 10 |
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10.3095869962 |
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*: trapezium integrate 0 1p1 10 |
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10.3871026879 |
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*: simpson integrate 0 1p1 10 |
*: simpson integrate 0 1p1 10 |
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10.3354255601 |
10.3354255601 |
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</lang> |
</lang> |
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Integrate <code>sin</code> from 0 to pi in 10 steps using various methods. |
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<lang j> |
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sin=: 1&o. |
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sin rectangle integrate 0 1p1 10 |
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2.00824840791 |
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sin trapezium integrate 0 1p1 10 |
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1.98352353751 |
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sin simpson integrate 0 1p1 10 |
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2.00000678444 |
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</lang> |
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Note that J has a primitive verb <code>p..</code> for integrating polynomials. For example the integral of <math>x^2</math> (which can be described in terms of its coefficients as <code>0 0 1</code>) is: |
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<lang> 0 p.. 0 0 1 |
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0 0 0 0.333333333333 |
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0 p.. 0 0 1x NB. or using rationals |
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0 0 0 1r3</lang> |
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That is <math>0x^0 + 1x^1 + 0x^2 + 0.3333x^3</math> |
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=={{header|Java}}== |
=={{header|Java}}== |
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